Ultrasonic Relaxation Study of 1-Alkyl-3-methylimidazolium-Based

Article pubs.acs.org/JPCB

Ultrasonic Relaxation Study of 1‑Alkyl-3-methylimidazolium-Based Room-Temperature Ionic Liquids: Probing the Role of Alkyl Chain Length in the Cation Michał Zorębski,† Edward Zorębski,*,† Marzena Dzida,† Justyna Skowronek,†,‡ Sylwia Jęzȧ k,†,‡ Peter Goodrich,§ and Johan Jacquemin§ †

Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland QUILL Research Centre, Queen’s University of Belfast, BT95AG Belfast, Northern Ireland United Kingdom

§

S Supporting Information *

ABSTRACT: Ultrasound absorption spectra of four 1-alkyl-3methylimidazolium bis(trifluoromethylsulfonyl)imides were determined as a function of the alkyl chain length on the cation from 1propyl to 1-hexyl from 293.15 to 323.15 K at ambient pressure. Herein, the ultrasound absorption measurements were carried out using a standard pulse technique within a frequency range from 10 to 300 MHz. Additionally, the speed of sound, density, and viscosity have been measured. The presence of strong dissipative processes during the ultrasound wave propagation was found experimentally, i.e., relaxation processes in the megahertz range were observed for all compounds over the whole temperature range. The relaxation spectra (both relaxation amplitude and relaxation frequency) were shown to be dependent on the alkyl side chain length of the 1-alkyl-3-methylimidazolium ring. In most cases, a single-Debye model described the absorption spectra very well. However, a comparison of the determined spectra with the spectra of a few other imidazolium-based ionic liquids reported in the literature (in part recalculated in this work) shows that the complexity of the spectra increases rapidly with the elongation of the alkyl chain length on the cation. This complexity indicates that both the volume viscosity and the shear viscosity are involved in relaxation processes even in relatively low frequency ranges. As a consequence, the sound velocity dispersion is present at relatively low megahertz frequencies. studies using the acoustic technique,1−4 only two papers have been published using an optic method to date.10,11 ILs are currently defined as molten salts with a melting temperature below 373 K. Simultaneously, salts that are liquid at room temperature form a subclass of ILs called room-temperature ionic liquids (RTILs).12,13 To the best of our knowledge, the available literature data on the ultrasound absorption are limited to only RTILs in practice. Apart from our previously reported results for 1-ethyl-3-methylimidazolium and 1-octyl-3methylimidazolium bis(trifluoromethylsulfonyl)imides ([C2mim][NTf2] and [C8mim][NTf2])2 as well as bis(1ethyl-3-methylimidazolium) tetrathiocyanocobaltate and bis(1butyl-3-methylimidazolium) tetrathiocyanocobaltate ([C2mim]2[Co(NCS)4] and [C4mim]2[Co(NCS)4]),1 only two other research groups have reported data obtained by means of a direct method based on the first travel pulse with a variable path length.3,4 For example, Makino et al.3 reported data for four imidazolium-based RTILs in the temperature range of 293−393 K but at three similar frequencies (e.g., 11.3,

1. INTRODUCTION Although relaxation processes in ionic liquids (ILs) have been extensively investigated over the last two decades using different experimental techniques, very few studies have been reported using an acoustic technique.1−4 However, the acoustic technique is also an interesting method because the ultrasound absorption is related to the energy dissipation caused by various irreversible processes taking place in the liquids. This energy dissipation results in the characteristic spectra, and a further analysis of such spectra, especially in a wide frequency range, can be an integral and significant source of valuable information regarding the molecular structure of the liquids, as well as the various physical and chemical processes occurring in the liquids at a nearly ideal thermal equilibrium.5 Ultrasound absorption investigations are also very useful and informative in the case of the pressure−temperature measurements of the speed of sound (an indirect route to obtain all of the observable thermodynamic properties of a fluid phase) as they must be carried out outside of the relaxation regions.6−8 Furthermore, knowledge of ultrasound absorption is necessary in some methods used for study of the nonlinear acoustic properties of the liquids.9 Unfortunately, there is a lack of ultrasound absorption in ILs data available in the literature. Apart from the above-mentioned © XXXX American Chemical Society

Received: December 26, 2015 Revised: March 16, 2016

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DOI: 10.1021/acs.jpcb.5b12635 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B 34.9, and 57.7 MHz), whereas Mirzaev and Kaatze4 studied ultrasound absorption of the ethylammonium nitrate (EAN) only isothermally (313.15 K) in the frequency range from 0.2 to 15 MHz. Using a transient grating (TG) method,14 additional experimental results have been reported by Frez et al.10 (for seven RTILs) and Kozlov et al.11 (for four RTILs). Unfortunately, in both cases measurements have been carried out only at a single frequency at 296.85 or 301 K, respectively. Generally, the TG method seems more suitable for measuring ultrasound velocity than the ultrasound absorption, and in the case of RTILs, a few such reports can be found.15−19 The above-mentioned study of the ultrasound absorption and the recently observed non-Newtonian behavior along with the lack of the dynamic crossover in the range of 1.2−1.5 Tg for [Cnmim]2[Co(NCS)4] (n = 2, 4)1 have been the motivation for a more detailed analysis of the role of the elongation of the alkyl side chain length in imidazolium cations on the molecular dynamics by a study of the ultrasound absorption and related properties for four consecutive (1-propyl, 1-butyl, 1-pentyl, and 1-hexyl) 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imides, i.e., [Cnmim][NTf2] (n = 3, 4, 5, 6). [Cnmim][NTf2] are hydrophobic RTILs that contain a large hydrolytically stable anion, and these RTILs are representative of a broad group of aprotic ILs. Worthy of note is that [C6mim][NTf2] is the reference substance recommended by IUPAC,20 and broadening its available property values as well as deeper knowledge about molecular dynamics may be additionally interesting to the research community. To complete the ultrasound absorption study and to obtain a set of consistent data, the speed of sound, density, and kinematic viscosity were measured as well. From the measurement results, the ultrasonic relaxation spectra, the differences between the experimental absorption and the classical absorption, the relaxation strengths, the ratios of volume and shear viscosity, as well as ultrasound velocity dispersion were calculated and analyzed in terms of differences in the length of the alkyl side chain of the imidazolium ring, together with the previously reported results for two other homologues of [Cnmim][NTf2] with (n = 2, 8)2 as well as [Cnmim]2[Co(NCS)4] (n = 2, 4).1 The results were compared with the behavior of imidazolium-based RTILs with hexafluorophosphate [PF6]− anion, i.e., [Cnmim][PF6] (n = 4, 6, 8) as well as [C4mim][NTf2] reported by Makino et al.3 In this work the term ultrasound velocity c is used in the case of being dependent on frequency of the phase ultrasound velocity of the longitudinal wave. Simultaneously, the speed of sound c0 is defined as being independent on frequency in the low-frequency limit of the phase ultrasound velocity.

2.2. Experimental Systems. In this work, both the ultrasound absorption and the speed of sound were measured by means of the so-called narrow-band technique. The ultrasound absorption measurements were carried out using a measuring set based on the standard pulse method with a variable path length. There are absolute measurements of the absorption coefficient α by variation of the sample thickness, where the α values are obtained from the slope of the straight line (amplitude of the received pulses versus sample thickness). The measurements within the frequency range 10−300 MHz were executed using two sets of broad-band ultrasonic heads (LiNbO3 transducers) mainly at a temperature range of 293.15−323.15 K and at atmospheric pressure. During the measurements, the temperature of the sample was maintained in each case with an uncertainty of ±0.05 K, and the measuring cell was filled with argon to avoid contact of the sample with air (hygroscopic nature of the samples). The uncertainty of the α· f−2 data was estimated to be ±2.5%. More details concerning the design and construction of the measuring set and the measurements procedure have been reported previously.22,23 The supplementary speed of sound measurements were carried out using a pulse-echo-overlap method. Our own measuring set (transmitting−receiving transducer with an acoustic mirror) operating at a fixed frequency of 2 MHz was used. For the calibration of the acoustic cell, redistilled and freshly degassed (by boiling) water (electrolytic conductivity 10−4 S·m−1) was used. During all measurements, the temperature of the sample was maintained by a cascade thermostat unit with fluctuations not exceeding ±0.05 K. The speed of sound measurements were done in a similar temperature range as in the case of ultrasound absorption. The uncertainty of the measured speeds of sound was estimated to be ±0.5 m·s−1. More details about the measuring set and method can be found elsewhere.24,25 The densities were measured with an Anton Paar DMA 5000 vibrating-tube densimeter, whereas the kinematic viscosities were measured using precalibrated Ubbelohde viscometers from Schott. The densimeter was calibrated with water and dry air. The densities were measured over a range of temperature of 70 K or more (up to 363.15 K), and in each case, the viscosity correction was made. For the kinematic viscosities, the measurements were done over a range of temperature of 40 K (from ca. 293 to 333 K), and if necessary, the Hagenbach correction for kinematic energy was applied. The temperature was maintained similar to those in the case of the speed of sound measurements, i.e., by a cascade thermostat unit with fluctuations not exceeding ±0.05 K. The uncertainty of the measured densities was ±0.05 kg·m−3. In turn, the uncertainty of viscosity was ±1%. During all experiments, temperature was determined according to ITS-90. Apart from the density measurements, temperature was determined using a certified (NIST) Pt 100 probe and a digital Ertco-Hart thermometer.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The RTILs used in this work were purchased from the QUILL Research Centre/School of Chemistry and Chemical Engineering, Queen’s University of Belfast. The liquids were synthesized and purified according to known procedures.21 The liquids were stored under argon, and the water content ( 4 and the ratio of the relaxation amplitudes fulfills condition 0.25 < A2/A1 < 4.46 When these conditions are not fulfilled, it may be impossible to resolve the contributions to the absorption spectrum from two processes (e.g., similar relaxation times), and the absorption data will have the appearance of a single relaxation curve. In principle, however, even the fact that the absorption data fit a single relaxation curve does not necessarily mean that there is in fact a single relaxation process. It should be noted here that apart from the traditional way of interpreting ultrasound absorption data, for theories of ultrasound absorption in liquids progress is very weak in practice. Indeed, an interesting statistical-mechanical theory for the description of ultrasound absorption in liquids on a microscopic level has been presented by Kobryn and Hirata,47 but its application in a real system remains a subject of future works. Although a direct comparison of the obtained ultrasound absorption spectra was not possible, the comparison with the ultrasound velocity dispersion reported by Fukuda et al.18 for [C4mim][NTf2] at 298.15 K shows some agreement, at least qualitative. According to Fukuda et al.,18 the ultrasound velocities are constant below 260 MHz within an experimental error, i.e., below 260 MHz the frequency dependence was not

lengths in the cation leads to the conclusion that the presence of the [PF6]− anion moves the relaxation region toward lower frequencies. Interestingly, both anions are halogenated and contain fluorine, but the [PF6]− anion is octahedral, relatively small, and more globular, whereas [NTf2]− is a nonglobular relatively large anion with the possibility of the internal rotations about the two S−N bonds (Figure S1). These rotations (clarified both theoretically36 and experimentally37) are a reason for a large internal flexibility of the anion, and its flexible nature is reflected in the occurrence of two equilibrium structures: cis and trans. At the same time, the activation energy (calculated by the use of eq 6) of the dissipative processes related to ultrasound absorption decreases with increasing frequency for each RTIL studied (Table S6). Interestingly, however, for frequencies below ca. 140 MHz Eα increases from [C3mim][NTf2] to [C6mim][NTf2], whereas for higher frequencies an inverse trend is observed, i.e., Eα decreases from [C3mim][NTf2] to [C6mim][NTf2]. Thus, at frequency in the vicinity of 140 MHz Eα is the same for each RTIL studied. Generally, the obtained ultrasonic spectra can be discussed assuming aggregation processes determined by Coulomb forces and dispersion forces as well as hydrogen bonding. The hydrogen-bonding contribution to the overall interaction energy in aprotic ILs is today widely accepted and well documented among others using far-infrared and terahertz spectroscopy (FIR and THZ) studies,38−40 and although such contribution is only about 10%, the nature of hydrogen-bond interactions (e.g., directional) can significantly influence the properties of such ILs. Generally, ILs can be treated as structured solvents (from ion pairs, ion clusters to H-bonded networks, micelle-like, and bicontinuous structures).13 The first suggestion of a bicontinuous structure considered to include polar and nonpolar regions was introduced by Schröder et al.41 Today, it is well established that the polar domains are not homogeneously distributed but form a continuous 3D polar network.13 These polar networks coexisted with nonpolar domains. However, in the case of short alkyl groups in imidazolium cations, small and globular nonpolar domains form within the polar network. In turn, when the alkyl chain length increases, the nonpolar domains interconnect in a bicontinuous sponge-like nanostructure. According to Canongia Lopes,42 this progression seems to be marked by the butyl side chain. Thus, assuming that aprotic RTILs studied can be treated as a mixture of polar and nonpolar domains, ultrasonic relaxation based on an equilibrium between these domains can be described by the discrete relaxation time according to eq 2 (i.e., by a single Debye-type relaxation term). The dynamics of the domain structure of ILs was recently investigated by Kofu et al.43 using the neutron spin echo spectroscopy (NSE). Data obtained using this technique, which is also able to investigate microscopic motions, show that the relaxation mechanism is most probably more complicated and cannot be assigned solely to the domain dynamics. This has been demonstrated by comparison of the shear viscosity relaxation and NSE results, which implies that the shear viscosity relaxation cannot be explained solely by the domain or microscopic structures.44 An analysis of the relaxation strengths (dependent on the enthalpy ΔH and volume ΔV change connected to the process disturbed by the acoustic wave) shows that the greatest r values are observed in the case of [C6mim][NTf2] (Table 3). This finding is not surprising taking into account that [C6mim][NTf2] shows highest compressibility (reflects volume changes G

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[C2mim]2[Co(NCS)4], whereas in the case of [C4mim]2[Co(NCS)4], lower frequencies (clearly below 100 MHz) were observed.1 This type of behavior has been observed in the past at similar temperatures for molecular organic liquids as well;23,49,50,55 however, it should be noted that a separate determination of the shear viscosity behavior requires a separate study of the shear ultrasound wave because ultrasound relaxation spectra determined using a longitudinal wave are not suitable to investigate the microscopic origin of the shear viscosity (there are difficulties in the separation of the contributions of volume and shear viscosities to the ultrasonic relaxation). It is a general agreement that if α < αcl, the shear viscosity relaxation must be present.1,2,5,23,49,50,55 Assuming that the shear viscosity relaxation is present and taking into account the simple Maxwell model, the real part η′(ω) of the complex (relaxing) shear viscosity can be expressed as

observed and a low-frequency limit of the ultrasound velocity (i.e., the c0 value) was attained. The ultrasound velocity dispersion calculations done by the use of a simple viscoelastic Maxwell model show some consistency but only at frequencies below 400 MHz,3 which is not especially surprising taking into account the used model. In turn, according to the simple Debye model used in this work for description of the ultrasound absorption data for [C4mim][NTf2] at 298.15 K, the relaxation frequency lies at 289 MHz. Thus, the results obtained by the use of different techniques are only consistent to a certain degree. As shown in Figure 8, the estimated dispersion curve

η′(ω) = ηS ·(1 + ω 2τM2)−1

(9)

where ω = 2·π·f and τM are the angular frequency and Maxwell relaxation time, respectively. The Maxwell relaxation time is defined as the ratio of ηS and the limiting shear modulus G∞ −1 τM = ηS ·G∞

(10)

Since the temperature variation of G∞ is usually much smaller than that of ηS, the τM is approximately proportional to ηS. The larger increase in ηS than the τM with lengthening of the alkyl chain in the imidazolium cation is interpreted as the decrease in G∞ with the increase of the chain length.51 The decrease in G∞ is also connected with the decrease in the Walden product and slight increase of the ratio of the shear viscosity and conductivity relaxation times τM and τΛ.51 According to Yamaguchi et al.,52 the increase in the length of the alkyl chain of the cation for [Cnmim][PF6] (n = 4, 6, 8) leads to the lower frequency shift of the shear relaxation frequency. At the same time, the shear relaxation frequency of [C4mim][PF6] also shifts to lower frequency in comparison to [C4mim][NTf2], i.e., the shear relaxation times of these two RTILs are evidently different, and this difference is connected to differences in the anions. Thus, the present results obtained from ultrasound absorption are consistent with the results reported for shear relaxation.52 The values of the ratios α/αcl in the nondispersion region below the relaxation frequency (Table 4) along with the negative temperature coefficients of ultrasound absorption α−1· (dα/dT) are typical for structural relaxation. From the ratio α/ αcl, the ratio ηv/ηs can be estimated from the following relationship

Figure 8. Ultrasound velocity dispersion at 293.15 K shown as difference c − c0 plotted against log f for (□) [C2mim][NTf2], (◊) [C3mim][NTf2], (Δ) [C4mim][NTf2], (■) [C5mim][NTf2], (○) [C6mim][NTf2], (●) [C8mim][NTf2], (▲) [C2mim]2[Co(NCS)4], and (●) [C4mim]2[Co(NCS)4]. (Inset) Dispersion beginning (in the increasing order) for (brown line) [C2mim][NTf2], (blue line) [C6mim][NTf2], (black line) [C8mim][NTf2], and (red line) [C4mim]2[Co(NCS)4].

for [C4mim][NTf2] indicates velocity dispersion at significantly lower frequencies than 260 MHz. A comparison between ultrasound velocity dispersion reproduction with the simple Debye model and previously reported in the literature dielectric relaxation48 led Fukuda et al.18 to conclude that in the case of [C4mim][NTf2] structural relaxation is much faster than reorientation relaxation, i.e., the relaxation is decoupled. On the other hand, both relaxations were strongly coupled in the case of [C4mim][PF6]. Fukuda et al.18 interpreted this difference as a result of the different anion structures. The obtained values of background absorption B for the highest investigated temperatures indicate that other relaxation processes can be present in the higher frequency range (B values are higher than values obtained by eq 5). On the other hand a clear indication of the non-Newtonian behavior is observed. Apart from [C3mim][NTf2], for the remaining three measured [Cnmim][NTf2], the α·f−2 values at lowest temperatures are in each case above frequencies of about 230 MHz (Figures 2−4) smaller than those obtained by the Stokes relation (eq 5). This means that a shear viscosity relaxation in the MHz range is present, and the frequency dependence of α·f −2 can also be closely connected with a relaxation behavior of the shear viscosity, i.e., in the considered frequency range the shear viscosity must decrease with the increasing frequency. A similar behavior has been reported for [C8mim][NTf2] where α < αcl was observed above ca. 150 and 180 MHz at temperatures of 293.15 and 298.15 K, respectively.2 At similar temperatures and frequencies, α < αcl was also observed in the case of

ηv /ηs = 4/3·(α /αcl − 1)

(11)

where ηv is the volume viscosity, which is a measure of the resistance of the liquid to a pure expansion or compression. It is worthy of notice that using the acoustic data is in practice the only way to determine the values of ηv, as they cannot be measured to date directly. The volume viscosity reflect the relaxation of both rotational and vibrational degrees of molecular freedom, whereas the shear viscosity reflects principally translational molecular motions as well as rotational motion through the translation−rotation coupling. The frequency independence of ηv was suggested as a necessary condition for claiming that the liquid is Newtonian.53 From this point of view, RTILs studied are obviously non-Newtonian. H

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The Journal of Physical Chemistry B Inspection of Table 4 shows that the obtained ηv/ηs values are around 1, which is similar for many associated molecular liquids.23 Thus, the magnitude of the ηv values is very close to that of the ηs values. Generally, if ηv/ηs is near 1 and approximately temperature independent (as in our case), it is well established for molecular liquids that a similar activation enthalpy for both viscosities can be supposed. Then a similar scenario may be present in the case of the aprotic RTILs studied; however, the temperature dependence of ηv/ηs shows a small increasing trend. This trend is very weak but suggests a small and increasing contribution from the aforementioned rotational relaxation process connected with the internal structures of anion. As known, in the case of isomeric rotational relaxation processes in molecular organic liquids, the ηv/ηs values are generally large and change with temperature changes.54 Generally, the results obtained in this work (Table 4) are in excellent agreement with the ηv/ηs values extracted from the ultrasound absorption data reported earlier2 for [C2mim][NTf2] and [C8mim][NTf2] because in the case of [C2mim][NTf2] we obtained 0.873 and 0.852 at temperatures of 293.15 and 298.15 K, respectively, whereas in the case of [C8mim][NTf2], we obtained 1.113 and 1.061, respectively. For three of four of the [C2mim]-based RTILs with different anions investigated recently by Kozlov et al.11 using a TG experiment, the ηv/ηs values are also in reasonable agreement. However, in the case of [C2mim][NTf2], the value ηv/ηs ≈ 0 (at 301 K) reported by Kozlov et al.11 is contradictory to the values (i.e., 0.873 and 0.852) extracted from a previous report.2 It should be noted that an approach used to determine the bulk viscosity by means of a TG experiment “may introduce a significant error”, as self-stated by Kozlov et al.11 4.3. Effect of Ultrasound Absorption on the Speed of Sound. Ultrasound velocity and absorption are two fundamental propagating parameters of an ultrasound wave. In real liquids, the intensity of a longitudinal wave decreases exponentially when passing through a liquid. Thus, the dissipation of energy from the ultrasound wave is in practice always present (the classical absorption is present in all liquids); however, the effect of ultrasound absorption on the speed of sound may be ignored so long as α ≪ ω·co−1 (or in a rearranged form so long as α·co·(2·π·f)−1 ≪ 1). For instance, at 2 MHz and 298.15 K in water, α = 0.085 m−1 and ω·co−1 = 8396.1 m−1. Moreover, in the same experimental conditions in ethanol α = 0.197 m−1 and ω·co−1 = 11004 m−1, in 1,2ethanediol α = 0.615 m−1 and ω·co−1 = 7594 m−1, in carbon tetrachloride α = 2.07 m−1 and ω·co−1 = 13643 m−1, and in 1,5pentanediol α = 4.11 m−1 and ω·co−1 = 7904 m−1. The data for the calculations were taken from the literature2,5,22,23 or measured during this study. Therefore, taking into account the four RTILs experimentally investigated in this work, it should be clearly noted that in the given experimental conditions the ultrasound absorption at low frequencies (i.e., at the frequencies used in typical speed of sound measurements, such as at 2 MHz) is also still small enough for correct use of the Newton−Laplace relation. In other words, c0 may be still treated as a thermodynamic equilibrium property because the effect of absorption on the speed of sound is small and may be ignored (dissipative processes can be neglected). This results from the fulfilled inequality α·co·(2·π·f)−1 ≪ 1, i.e., the left side values always lie in the range from 1.3 × 10−4 (the lowest value, [C3mim][NTf2] at 323.15 K) to 5.9 × 10−4 (the highest value, [C6mim][NTf2] at 293.15 K); generally speaking, over the whole investigated

temperature range these values are in great part somewhat higher than for carbon tetrachloride at 298.15 K (1.52 × 10−4) and lower than for 1,5-pentanediol at 298.15 K (5.2 × 10−4). However, in many liquids, a relaxation process or even several relaxation processes are responsible for additional, often strong increases of ultrasound absorption. In these highly attenuating conditions as well as in the border regions, particular care must be exercised because the relaxation processes cause not only absorption but also dispersion.55,56 In the case of the four measured RTILs, the lowest f rel values associated with ultrasound absorption are 169 and 172 MHz, which are observed for [C5mim][NTf2] at 288.15 K and [C6mim][NTf2] at 293.15 K, respectively; however, still lower f rel values are observed at room temperatures in the case of [C8mim][NTf2] and [Cnmim]2[Co(NCS)4]) (Table S8). Since (i) the relaxation frequency associated with the ultrasound absorption decreases with decreasing temperature (and vice versa), (ii) the α/αcl is small (in the range 1−3) and practically independent of temperature, and (iii) the temperature coefficient of ultrasound absorption is negative, the close similarity of ultrasound absorption in RTILs studied and associated molecular liquids is observed (the similarity was suggested already in our previous reports1,2). In other words, this is the same group according to liquid classification in relation to ultrasound absorption.55,56 Since the relaxation frequency decreases with increasing pressure in associated molecular liquids,55,57 we can suppose with the great probability that both RTILs studied to date and generally all aprotic RTILs behave similarly. Obviously, it is only supposition, but it is plausible. As mentioned in the Introduction, knowledge of the relaxation regions is necessary to correctly use the acoustic method (based on the speed of sound measurements) to obtain related thermodynamic properties under high pressures because such studies must be done outside of the relaxation regions of the ultrasound velocity.6−8 Unfortunately, this crucial condition can sometimes be overlooked. In other words, it should be kept in mind that for all aprotic RTILs studied to date the determined f rel decrease with decreasing temperature and increasing side alkyl chain length in 3-methylimidazolium cation (refs 1−3 and this work) and f rel should decrease with increasing pressure. Thus, care must be exercised when investigating RTILs in lower temperatures and/or higher pressures. For instance, for [Cnmim][NTf2] homologues it is especially important beginning from [C6mim][NTf2], whereas in the case of [Cnmim][PF6] homologues it begins even from [C4mim][PF6]. In the case of [Cnmim][PF6], the clear dispersion symptoms are visible for [C6mim][PF6] and even more for [C8mim][PF6] already from temperatures near 300 K at atmospheric pressure because the measured speed of sound shows an increase of deviations from linearity (much more evident in the case of [C8mim][PF6]) with decreasing temperature.3,58 In other words, the lower the temperature the higher the increase of the speed of sound with decreasing temperature (concave up curve) is observed, and it is typical behavior in dispersion regions.54,55 In the case of [C8mim][PF6], an additional argument for the existence of a relaxation region in the range of several MHz is connected with the shear relaxation spectra which indicate, for instance, the shear relaxation frequency is already around 20 MHz at 298.15 K.44 Therefore, in practice it is always necessary to exercise caution whether the measured speed of sound in the given experimental conditions (lower temperature and/or high pressure) can be I

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Table 5. Dispersion Values c∞/co for Various RTILs at Temperature 298.15 K, Obtained Directlya from Measurements of the c∞ and co Using the TG Method as Well as Indirectlyb by Estimation from Ultrasound Absorption Measurements

indeed treated as the equilibrium thermodynamic quantity and used to determine the thermodynamic properties under high pressures by means of an indirect acoustic route. It is especially important in the case of ILs showing high viscosities and/or rapid increase of viscosity with decreasing temperature. Because of the relatively large ultrasonic absorption in many RTILs, ultrasonic velocity is subject to a considerable dispersion. Fortunately, from the ultrasound absorption data, the frequency dependence of the ultrasonic velocity can be estimated.55,59,60 Figures 8 and 9 show examples of the

RTIL

c∞/co

[C4mim][BF4] [C4mim][PF6]

1.13a 1.16a 1.22a 1.14a 1.008b 1.017b 1.024b 1.07a 1.22 1.031b 1.033b 1.034b 1.034b 1.059b 1.26a

[C4m2im][BF4] [C2mim][NTf2] [C3mim][NTf2] [C4mim][NTf2]

[C5mim][NTf2] [C6mim][NTf2] [C8mim][NTf2] [C2mim]2 [Co(NCS)4] [C4mim]2 [Co(NCS)4] [N1,1,1,3][NTf2]

ultrasonic velocity dependence on frequency estimated from the absorption data by use of the following relation −1

work work work

work work work work work

ultrasound absorption data above 300 MHz and the fact that none of the absorption spectra reach the frequencyindependent high-frequency limit, which results in greater uncertainty of the estimated c values in the high-frequency region, and especially c∞, and (ii) on the other hand, the c values in the high-frequency region along with limiting c∞ values determined using the TG method are also connected with relatively great uncertainty. Finally, we must explain that only originally calculated sets of parameters of ultrasound absorption spectra were discussed because of the small effect on these spectra resulting from consideration (or not) of the ultrasound dispersion.

Figure 9. Ultrasound velocity dispersion shown as difference c − c0 plotted against log f for [C6mim][NTf2] at temperatures (□) 323.15, (◊) 313.15, (Δ) 303.15, (■) 298.15, and (○) 293.15 K.

n

refs 15 15 18 15 this this this 15 18 this this this this this 18

2

Ai ·f rel, i ·f c0 c2 1 = + · ∑ −2 π i = 1 1 + (f 2 ·f rel, c02 ) ·(1 − Ai ·c0·frel, i ·π −1) i (12)

5. CONCLUSIONS Frequency-dependent absorption is a characteristic acoustic property because the experimental data clearly do not show a constant α·f−2 but instead exhibit d(α·f2)/df < 0. In the investigated temperature range, d(α·f−2)/dT < 0 is observed as well. Moreover, the results show that lengthening the side alkyl chain in 1-alkyl-3-methylimidazolium cations does not show a significant effect on the speed of sound but significantly affects the ultrasound absorption spectra (both relaxation amplitude and relaxation frequency). Whereas the relaxation frequency decreases with increasing chain length, i.e., with increasing of the nonpolar part of the cation, the magnitude of α·f−2 clearly increases regularly with the increasing length of the side alkyl chain of the 1-alkyl-3-methylimidazolium cation. From the [Cnmim][NTf2] measured in this work and the literature data, the highest absorption and lowest relaxation frequency were observed for [C8mim][NTf2]. All of the findings can be generally attributed to the clear shift in balance between the polar part and the nonpolar part of the imidazolium cations. Lengthening the side alkyl chain of the imidazolium cation increases the nonpolar part of the cation and consequently leads to the increase of the entire nonpolar domain. It should also be noted that the longer the carbon chain the more important the internal motion of the molecule with respect to the Coulomb interactions as well as to the possible hydrogenbonding association. Qualitatively, the described behavior is independent of the anion because the literature data on

where Ai and f rel,i denotes the parameters obtained from the ultrasound absorption data. The n number is the same as in the case of the model used for description of the ultrasound absorption data, i.e., the use of eq 3 (single Debye term) leads also to n = 1 in eq 12. Thus, it is not surprising that the frequency dependence of c is strongly correlated with the relaxation frequency (or frequencies) of the relevant absorption spectrum. From the eight RTILs for which the dispersion curves of ultrasonic velocities were estimated, [C4mim]2[Co(NCS)4] shows ultrasonic velocity dependence on frequency as early as above 7 MHz at 293.15 K. At the same temperature, [C6mim][NTf2] shows such dependence above 28 MHz; however, with increasing temperature, the dispersion region is shifted rapidly toward higher frequencies, i.e., above 100 MHz at 323.15 K (see Table S9). At the same time the weakest dispersion (starting about 80 MHz at 293.15 K) shows [C2mim][NTf2]. As an indication of dispersion was taken into account the estimated values for which the difference between these values and the determined experimentally speed of sound (c − c0) exceeded the uncertainty of the experimental speed of sound equal ±1 m·s−1 (U(c0) = 0.5 m·s−1, k = 2). Table 5 summarizes the dispersion values c∞/c0 obtained both indirectly from absorption measurements and directly from the TG method. It is visible that the dispersion obtained indirectly is somewhat lower than those obtained from TG measurements. This discrepancy results probably from two basic reasons: (i) on one hand, it is connected with the lack of J

DOI: 10.1021/acs.jpcb.5b12635 J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B ultrasound absorption for [Cnmim][PF6] and [Cnmim]2[Co(NCS)4] analyzed in this work suggested the same results; however, for the same cation, the magnitude of α·f−2 in the nonrelaxation region below the relaxation frequency is clearly lower in the case of the [NTf2]− anion in comparison with the [PF6]− anion. In other words, [Cnmim][NTf2] showed a lower absorption than adequate [Cnmim][PF6]. Thus, the energy dissipation associated with both the classical and the nonclassical contributions increases with increasing alkyl chain length of the 1-alkyl-3-methylimidazolium cation and with a change of the anion from [NTf2]− to the [PF6]−. Furthermore, these RTILs show mostly both the structural and the shear relaxation processes. Thus, the results of the ultrasound absorption investigations (longitudinal wave) are consistent with the literature reports on shear relaxation spectra (transversal (shear) wave). The analysis of the ultrasound velocity dispersion for [Cnmim][NTf2] and [Cnmim]2[Co(NCS)4] shows that in experimental conditions dispersion is already present at relatively low megahertz frequencies; the strongest shows [C4mim]2[Co(NCS)4] starting already from a frequency above 7 MHz at 293.15 K, whereas the weakest shows [C2mim][NTf2] starting from a frequency in the vicinity of 80 MHz. An additional analysis of the effect of ultrasound absorption on the speed of sound showed that in the given experimental conditions use of the Newton−Laplace relation to determine the thermodynamic properties is rather well founded and correct. However, at lower temperatures and/or higher pressures special care must be exercised. Generally, special care must be exercised when the speed of sound measurements are planned or made for RTILs showing high or extremely high viscosities. In such situations, the measurements in a broader temperature range, especially also at higher temperatures, are suggested, and next, the linearity should be checked and analyzed. It is the simplest and also a plausible solution in the case of the controversy on the presence of strong dissipative processes during ultrasound wave propagation.

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ACKNOWLEDGMENTS

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REFERENCES

The authors are grateful to Mr. A. Praski for the viscosity measurement.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b12635. Characterization, structure, and synthesis of [Cnmim][NTf2] (n = 3, 4, 5, 6), the raw values of speed of sound, density, viscosity (kinematic and static shear), quotient α·f −2, activation energy Eα, isentropic compressibility (coefficient and molar), and dispersion start as well as refitting results reported in refs 1 and 2 for [C8mim][NTf2] and [Cnmim]2[Co(NCS)4] (n = 2, 4) by use of the model with two Debye terms (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +48 323591625. Fax: +48 322599978. E-mail: emz@ ich.us.edu.pl. Author Contributions ‡

J.S. and S.J. contributed equally to this work.

Notes

The authors declare no competing financial interest. K

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